QUALITY IMPROVEMENT OF OBJECT EXTRACTION FOR KEYFRAME DEVELOPMENT BASED ON CLOSED-FORM SOLUTION USING FUZZY C-MEANS AND DCT-2D.

ISSN 0216 – 0544

Vol. 7, No. 2, July 2013

QUALITY IMPROVEMENT OF OBJECT EXTRACTION FOR
KEYFRAME DEVELOPMENT BASED ON CLOSED-FORM
SOLUTION USING FUZZY C-MEANS AND DCT-2D
a

Ruri Suko Basuki, bMochamad Hariadi, cMauridhi Hery Purnomo
a,b,c
Faculty of Industrial Technology, Dept. of Electrical Engineering Institut Teknologi Sepuluh
Nopember, Kampus ITS Keputih, Sukolilo, Surabaya, Jawa Timur, Indonesia
a
Faculty of Computer Science, Dian Nuswantoro University
Jalan Imam Bonjol, Semarang, Indonesia
E-mail: arurisb@research.dinus.ac.id
Abstrak
Penelitian ini bertujuan untuk meningkatkan kualitas ekstraksi obyek pada citra tunggal hasil
pemecahan frame dari video sekuensial yang terkompresi. Kualitas hasil ekstraksi obyek
dengan algoritma closed-form solution menurun karena adanya beberapa perubahan nilai

intensitas pada channel RGB. Sehingga di sekitar batas tepi obyek hasil ekstraksi terlihat
kasar baik secara visual maupun hasil pengukuran dengan Mean Squared Error (MSE)
antara obyek hasil ekstraksi dengan ground truth. Untuk meningkatkan kualitas hasil
ekstraksi objek, nilai threshold pada unknown region ditentukan melalui adaptive threshold
yang diperoleh dengan mengaplikasikan algoritma Fuzzy C-Means (FCM). Pemilihan
algoritma FCM karena dalam penelitian sebelumnya algoritma ini menunjukkan hasil yang
lebih robust dibandingkan algoritma Otsu untuk mendapatkan nilai threshold yang optimal.
Sedangkan untuk menghaluskan obyek di sekitar daerah batas tepi digunakan filter Discrete
Cosine Transform (DCT) – 2D. Dari 10 obyek yang digunakan dan dievaluasi dengan MSE
menunjukkan peningkatan rata-rata sebesar 31.55%. Namun pendekatan ini tidak begitu
robust pada citra yang memiliki kemiripan warna. Penggabungan pendekatan ini dengan
optimasi cost function dalam alpha region pada basis spectrum diharapkan mampu
meningkatkan kinerja algoritma ekstraksi obyek pada penelitian selanjutnya.
Kata kunci: Closed-form Solution, Algoritma Fuzzy C-Means, Discrete Cosine Transform-2D.

Abstract
The research is aimed to improve the quality of the extraction of the object in a single image
resulted from frame’s fragmentation of sequential compressed video. The quality of the
extracted objects with closed-form solution algorithm decreased due to some changes in the
intensity values on the RGB channel. Thus, the extraction result around the boundary edges

of objects visually seemed to be rough and when it was measured with the Mean Squared
Error (MSE) beween the object extraction results with ground truth. To improve the quality
of the extracted object, the threshold value on unknown region was determined by adaptive
threshold obtained by applying the Fuzzy C-Means algorithm (FCM). FCM algorithm is
chosen since in the previous research this algorithm gives more robust results than Otsu
algorithm to obtain the optimal threshold value. Meanwhile, to eliminate noise around the
border area, this research applies Discrete Cosine Transform (DCT) - 2D filters. The result
of 10 objects used and evaluated with the MSE showed an average increase of 31.55%.
However, this approach is not so robust to images having similar color. Combination of this
approach with optimization of the cost function on the alpha region based on spectrum is
expected improving the performance of object extraction algorithm for the next research.
Key words: Closed-form Solution, Fuzzy C-Means Algorithm, Discrete Cosine Transform-2D.

89

90 KURSOR Journal Vol. 7, No. 2, July 2013, page 89-98

INTRODUCTION
The emergence of digital television standard
such as Digital Television (DTV) in

America, Digital Video Broadcasting –
Terrestrial (DVB-T) in Europe and Integrated
Services Digital Broadcasting - Terrestrial
(ISDB-T) in Japan rise the rapid demand of
multimedia technology. The rapid increase of
multimedia data exchange based on
networking encourages the emerging of
video coding standard.
Several methods of video coding
standards such as H.261, H.263, MPEG-1
and MPEG-2 have been extensively used in
DVD, digital television, video conferencing
and some application in telemedicine [1].
The simple method in computation, however,
has not been able to fulfill the users
requirements.
Currently, the new model of video
standard defined by MPEG-4 and MPEG-7
provides
standard

technology
for
representation and video data manipulation
[2]. One of the important innovations in the
MPEG-4 standard is the ability to manipulate
object in image sequences. Scene description,
a video or audio object that correlated with
the technique of organizing objects in a scene
can be encoded with this standard [3,4].
Meanwhile, the MPEG-7 standard supports
indexed multimedia
database
and a
structured meta data provides a rich media
content in semantic view.
The function of the object-based
technology can be used in computer vision
applications such as object extraction, motion
understanding, images recognition, and
augmented

reality.
However,
object
extraction process on video data will be a
difficult job, since it has no semantic
information. Indeed, the process of object
extraction is an ill-posed problem [5],
whereby only human perception
can
understand of the semantic meaning of the
video object. For instance, in the process of
video editing, pullout of objects are often
done by manual segmentation. Therefore, a
video objects semantic can only be identified
by human vision by considering video
context. So it is not effective in applying the
action to large volume video data.
In recent years, several algorithms have
been developed to overcome the problems of

video object segmentation. Based on user
interaction, the technique can be classified
into an automatic (unsupervised) and semiautomatic (supervised)
category.
An
automatic object extraction doesn't require
human intervention in the extraction process.
It uses special characteristic of the scene or
specific knowledge such as color, texture and
movement. Therefore, it is difficult to do
the semantics from the object segmentation,
because it is possible to have some color,
texture and movement [6]. For these reasons,
a semi-automatic approach to extract the
object (supervised)
involving human
intervention is proposed by combining
human perception (manual segmentation) and
automatic segmentation.
During the segmentation process on the

semi-automatic object extraction method
(supervised),
human intervention
is
involved in several stages to provide a direct
semantic information. When semantic of the
video object is provided by user, the
mechanism of object tracking is done by
following the temporal transformation in
subsequent frames. Generally, the tracking
process are prone to error due to the
degradation of intensity value of reference
frame. Therefore, users need to make
improvement on semantic information by
refreshing the keyframe at specific locations
in a video sequence.
In this paper, we propose the techniques
to improve an object extraction quality for
keyframe which can be applied in a semiautomatic video object extraction. Extraction
process on the single image is performed by

closed-form solution approach [7]. To
distinguish the objects and background in
the image (single frame), it is done by
applying the interactive matting using a
scribble technique as an interface [8]. This
approach produces impressive results in the
implementation
in
the
raw
image
(uncompressed image). However, this
method is not robust to handle the
compressed image sincethe extraction result
seems rough. It occurs due to the changes in
the intensity values at each pixel, so that
when the image is displayed in a histogram
graph it turns towards the contrast. To
improve the extraction quality, we propose
the adaptive threshold for determination

threhold value in the unknown area and

Basuki et.al., Quality Improvement of …91

remove the noise on
extracted object.
Furthermore, an accuration of the object
extraction based on spectrum using closedform solution is be improved.
The organization of this paper as follows :
The second section explains the closed-form
solution algorithms for basis system, and also
describes
the
adaptive
threshold
determination and noise reduction quality
improvement for object extraction. The third
secgtion describes framework of the
extraction system. The fourth section
describes our experiments and also evaluate

the performance of our algorithm. The fifth
section provides conclussion and future work
discussion of our paper.

Matting Process
The object extraction in image and video is
interesting object to be analyzed. Porter and
Duff [7,9,10] introduce alpha channel used as
tool to control linear interpolation of the
foreground and background color. Then
alpha channel is described as matting
algorithm by assuming that every pixel Ii in
input image is linear combination of
foreground Fi and background Bi color.

Ii  i Fi  1  i  Bi ,

where 0    1 (1)
By compositing Equation (1), it is assumed
that every pixel is a convex combination of

layer K image F 1 ,, F k as noted in
Equation (2).
K

(2)

k 1

Vector K from  k is the matting
component of image determining fractional
contribution from each layer observed in
each pixel.

Spectral Analysis
Generally, spectral segmentation method is
associated with image with A matrix affinity
size N  N , which is assumed as

A(i , j )  e

 dij / 2

where D is matrix degree from graph that is
shown in Equation (4).

G  V , E  withV  n

(4)

And D is diagonal matrix as seen in Equation
(5).

Di , j   A  i, j  ,

(5)

j

 deg  vi  if i  j
where di , j  
Otherwise
0
D(i , j ) is filled with degree information of
each vertex (node) with D for G a s
that is
rectangular matrix size n  n
described. Thus, L is symmetric positive

THEORITICAL BACKGROUND

I i   ik Fi k

pixels (e.g. color and geodesic space), which
is defined in Equation (3).
(3)
L  D – A

and d ij is the space among

semi-definite matrix which the eigenvector
catches many image structures. The affinity
matrix A is able to catch the information
that an image consists of some different
clusters or connected component. Subset C
in image pixel is the connected component of
image A(i , j )  0 for each (i, j ) so i  C
and j  C . Thus, there is no subset C which
is able to fulfill this property. If the indicator
vector of component C is noted as mC , see
Equation (6) thus

1 i  C
miC  
0 i  C

(6)
m represents 0-eigenvector (eigenvector
with eigenvalue 0) from L . In the
assumption that image consists of connected
component K , C1 ,, CK to
C

with Ck disjoint subset on pixel.
The indicator vector m 1 ,, m K resulted
from eigenvector calculation on L is only
reaching the rotation, since the rotation of
matrix R in size K  K , and vector
[mC1 ,, mCK ]R is the nullspace base on L .
The different components extraction of the
smallest eigenvector is called as “Spectral
Rounding” and it becomes the concern for
some researches [11-15]. The simple
approach for clustering pixel image uses KC

C

92 KURSOR Journal Vol. 7, No. 2, July 2013, page 89-98

Means algorithm [11] and perturbation
analysis to limit algorithm mistake as
connectivity function in and among clusters.

Matting Laplacian
Matting Laplacian [7] is used for evaluating
the matte quality without estimating
foreground and background color as in
Equation (7). It uses local window w
forming two lines which is different in RGB
domain. The α in w stated as linear
combination of color channel.
i  w i  a R IiR  aG IiG  a B IiB  b (7)
The matte extraction problem becomes one
of the findings in alpha matte minimizing the
deviation of linear model (previous equation)
in all image windows wq as shown in
Equation (8).
2

   aR I R  
J  , a, b     G Gi qB i B
   aq

qò I iò wq  aq I i  aq I i  bq 

2

(8)

color vector in al pixel q ,
is matrix
covariant size 3  3 in the same windows,
is the sum of pixels in window, and I 3 is
identity matrix size 3  3 . By the
occurrence of the smallest eigenvector, the
other use of matting Laplacian property (eq.
10) is to catch information of job fuzzy
cluster on image pixel, including the
calculation before the limit determent by user
is specified [13].

Linear Transformation
Seeking linear transformation in eigenvector
will result a set of vector in which the value
is closed to binary. The formula is noted as
E  [e1 ,, ek ] become matrix N  K of
eigenvector. Then, in finding a set of linear
combination K , vector
y k minimizes
Equation (11).


i ,k

is the regularization requirement of
 . The coefficient of linear model  ,b
enables the elimination from Equation (8),
and results quadratic cost in α.

J     L ,
T

(9)

Cost function as seen in Equation (9) has
minimum trivial that is the vector. Then, in
framework user-assisted [13], J   is the
subject minimized in user constraint. L is
matting Laplacian. Symmetric semi-definite
positive matrix N  N is the matrix
inserting input image function in local
windows, depending on unknown foreground
and background color in the coefficient of
linear model. L variable is defined by the
sum of matrix
in which on each is
filled with affinity among pixels in local
window wq as seen in Equation (10).
1





  1 1   I   T    I   I     ,
 ij

i
q
j
q
3x3




wq
Aq  i, j    wq 
 q




0 Otherwise


where  i, j   wq

 ij is Kronecker delta,  q is

(10)

the average

k 
i



 1   ik , where k  Ey k

subject to ik  1

(11)

k

If 0    1, thus, the value of   0,9 , then
is robust measurement
value in matting component [10]. The result
of Newton process depends on initialization
process since the cost function (eq. 11) is not
convex. The K-means algorithm is applicable
in the initialization process on the smallest
eigenvector in matting Laplacian and
projects indicator vector of cluster resulted
from eigenvector E is shown in Equation
(12).

 k  EET mC

k

(12)

The matting component result is then added
so that it gives solution in (see Equation
(11)).

Grouping Component
The complete extraction result of foreground
matte is determined by simple sum of
components in foreground. For example,
 k1 ,,  kn
is design as foreground

Basuki et.al., Quality Improvement of …93

 x11
x  
 xm1

component as seen in Equation (13).

    
k1

kn

(13)

If the smallest eigenvector is not equal to
zero, the measurement of result quality  matte is done by  T L , in which L is the
matting Laplacian. The first calculation of
correlation among matting component and L
and deviation in matrix K  K is defined in
Equation (14).

  k , l    kT L l

(14)

Then matte cost is calculated in Equation
(15).

J    bT b
where b is the binary vector of
dimensional
indicating
the
component.

(15)
Kchosen

(18)

And matrix of cluster center defined in
Equation (19).

 v11
v  
vm1

v1m 


vmm 

(19)

The minimum objective function indicates
the best clustering result, therefore (see
Equation (20)).
*

*

J m* (U ,V ; X )  min J (U ,V ; X ) (20)
if dik  0, i, k ; m  1 , and X has at least

m elements, then (U ,V ) can minimize J m
with the condition as seen in Equation (20)
and Equation (21).
m

 j 1

Fuzzy C-Means (FCM) Algorithm
Cluster center of the FCM algorithm initially
was performed to mark the location of the
average of every cluster. In these conditions,
the accuracy of the cluster centers is
inaccurate, since each data has a degree of
membership in every cluster. Accuracy
improvement at the cluster center is
performed by minimizing the objective
function; see Equation (16), which is
performed repeatedly in order to move
towards the cluster center in the right
position. The objective function [16] is
denoted in Equation (16) and Equation (17).
n

x1m 


xnm 

c

2
m
J m U ,V ; X     ik  ' dik  , m ' (1, ) (16)
k 1 i 1

where
1/2

m
2
dik  d  xk  vi     xkj  vij   (17)
 j 1

The objective function J m can have a large
number of values, however only the smallest
one related to the best clustering, therefore it
is needed to find the most optimum value of
the large number of possible values.
Euclidean distance is used to measure the
distance between the th cluster center and
the th data sets [16]. The matrix data is
denoted in Equation (18).

ik 

and




1
m 1

kj

2


X ij V kj 




    ik  X
n

kj

ij

m


k 1 
 j 1
m

V

 X V 

i 1







1
m 1

m


n

i 1

ik



m

ij

(21)

;1  i  m;1  k  n



(22)
 ;1  i  m;1  j  m

Discrete Courier Transform-2D
DCT - 2D (Discrete Cosine Transform 2D) is applied to reduce noise around the
edge boundary of the foreground, which is a
direct extension of the 1-D case and is given
in Equation (23)/
f  x, y  cos
N 1 N 1
(23)
C  u, v   α  u  α  v    π  2 x  1 u   π (2 y  1)v 
cos
y 0 x 0







2n



2n



u, v  0, 1, 2, , N – 1 ,  (u ) and
are
defined in Equation (24).
 (v )

for





α  u  




1
N

for u  0

(24)

2
N
for u  0

The inverse transformation is defined in
Equation (25).

94 KURSOR Journal Vol. 7, No. 2, July 2013, page 89-98

N 1 N 1

  u)α (v  C  u, v  cos

f  x, y     π  2 x  1 u 
 π  2 y  1 v 
y 0 x 0 
 cos 
,
2n
2n





(25)
for x, y  0, 1, 2,.. , N  1 .
The 2-D basis functions can be generated by
horizontally multiplying the basic functions
as in the 1-D with a vertical set oriented of
similar functions [17]. Progressive increase
in frequency occurs both in the vertical or
horizontal direction as the basic function for
N = 8. The top left of the basic function is the
result of multiplying the DC component

OBJECT EXTRACTION SYSTEM
In this section, the proposed object extraction
framework for compressed image
was
performed in the steps, as depicted in figure
1.
Compressed
image (single
frame)
Convert to grayscale
image
Threshold
determination using
FCM
Matting object using
closed-form solution
Filtering
using DCT2D
Evaluation of
extraction
results

Figure 1. Object Extraction Stages.
The raw video data was fragmented into
the frame and compressed in a single image
(ilustrated in figure 1). The first image was
converted into grayscale . Furthermore, the
grayscale image was used as data matrix (eq.
18) and FCM [18] was applied to obtain the
objective function (eq. 16).

The previous method [7, 10], the
extraction process is performed by deriving
the cost function in alpha, whereas the
optimal cost function was obtained by a
sparse linear system. In our work, the
objective function of the FCM is applied to
determine the best threshold instead of using
a sparse linear system. Object extraction is
performed by considering a user-spesified
constraint on the foreground and background
areas (white scribble representing foreground
and black represents the background). A new
closed-form solution approach, which is used
as the basis in this study was applied to draw
"matte" of the whole image.
Finally, the evaluation of the performance
of the system is performed by comparing the
extracted objects with ground truth.

RESULT AND DISCUSSION
In our experiments, we applied the MPEG-4
standard tests for video sequences obtained
from the UCF Sports Action Data Set. At the
first stage, we splited a video into several
frames and used the first frame as the
analyzed frame (see Figure 2). The first
frame was extracted with a closed-form
solution approach [7]. Initially, we used first
frame as input image and scribble image as
depicted in the Figure 3.a and 3.b. Object
separation is performed by pulling “matte" of
the whole image. It is performed by
considering the alpha value
in the
Equation (1) which is obtained by the cost
function in the Equation (9). The value of the
cost function greatly affects accuracy of
matte extraction. To optimize the cost
function, [7,10] used a sparse linear system.
The results are quite impressive when applied
to the raw image data (describe in Figure
3.c).
However, the techniques were not robust
as it was implemented in a compressed image
(such as object extracted in Figure 3.d). It
occured since the intensity values in each
channel for some pixels in the compressed
image, was change. The changes were
presented in the form of a histogram which
was comparing the frequency of intensity
value
between raw image and the
compressed image. (shown in Figure 4.a, b,
c).

Basuki et.al., Quality Improvement of …95

Figure 2. Frame separation of the video sequences

(a)

(b)

(c)
(d)
Figure 3. (a) Input Image, (b) Scribble Image, (c) Object Extracted from the Raw Image, (d) Object
Extracted from the Compressed Image.

(a)

(b)

(c)

Figure 4. The Changes in Intesity : (a). Red Channel, (b). Green Channel, (c). Green Channel.

96 KURSOR Journal Vol. 7, No. 2, July 2013, page 89-98

(a)
(b)
(c)
Figure 5. (a) Compressed Image, (b) Extracted Objects with Closed-Form Solution, (c) Extracted
Objects with Our Approach.

(a)
(b)
(c)
Figure 6. MSE Value Between the Extracted Object and Ground Truth : (a). Red Channel,
(b). Green Channel, (c). Blue channel
Table 1. The Value of MSE between the Extracted Object and Ground Truth
Image
Playing Golf
Football
Running
Diving
Swing
Skateboarding
Lifting
Walkfront
Karate
Riding Horse

Red
Channel
7.79
11.07
11.37
11.49
12.74
16.12
17.54
20.53
25.22
42.97

Closed-Form Solution
Green
Blue
Channel
Channel
7.17
5.94
14.42
8.34
11.45
11.37
9.36
8.47
11.50
12.13
16.27
16.10
10.56
9.28
17.95
15.51
21.19
27.03
46.99
51.18

Red
Channel
6.69
4.49
7.69
8.52
8.07
9.65
15.99
16.30
17.51
30.40

Our Approach
Green
Channel
6.07
5.57
7.76
5.69
7.21
9.85
9.80
13.14
13.90
32.13

Blue
Channel
4.85
4.43
7.71
5.23
8.19
10.41
8.76
9.71
19.00
33.33

Basuki et.al., Quality Improvement of …97

To improve the ability of the previous
algorithm, we applied FCM [18] threshold
which is applied in the cost function and
DCT-2D to filter noise around edge
boundary. FCM algorithm comprises the
following stage:
1. Specify the data to be in the cluster,
namely n  m matrix (n = number
of sample data, m = attribute each
data).
sample data th (i=1,2,3 ....
n), attribut th (j = 1,2,3....m).
2. Determine :
- Number of cluster
- Grade
- Maximum iteracy
- The smallest expected error
- Initial objective function
- Initial iteracy
3. Generate random numbers
,
=1,2,3....n, =1,2,3....c as initial
elemen of
matrix. Calculate the
amount of each column by Equation
(26).
c

Q  
i

k

ik

(26)

, k  (1, 2,3...c)

4. Estimation the cluster center using
Equation (22), where k=1, 2, 3...c and
j=1, 2, 3...m.
5. Calculate the objective function by
Equation (27)
2
n
c  m
m  (27)


P      X ij V kj     ik 
t

i 1 k 1



j 1




6. Calculate the change of the matrix
partition using Equation (21), where
i=1, 2, 3...n and k=1, 2, 3...c.
7. Check the stop condition :
- If
   1    or

P P
t

-

t

 t  MaxIter  then stop
Otherwise :  t  t  1 :

go to

step – 4.
Next, the value of the FCM threshold is
considered as a cost function in alpha

parameters of the closed-form solution
approach. Extraction results are depicted in
Figure 5.b. To reduce the noise around edge
boundary of the extracted object, we applied
DCT-2D as seen in Equation (23), Equation
(24), and Equation (25). The final result is
illustrated in Figure 5.c.
We evaluated the extraction results of the
experiments by using MSE (Mean Squared
Error) as in Equation (28).
MSE 

( i 1 j 1[Grd .imgi , j   Ext.Obj(i , j ) ])

(28)

NM

is the ground truth image resulted
from the object extraction of the raw data.
Whereas
is the new image
generated from the extraction process [19].
The value of MSE between the raw image
and compressed image is described in Table
1. The improvement of extraction results of
each channel was depicted in the Figure 6.

CONCLUSION
In this paper, we proposed an approach to
increase the object extraction quality by
using the FCM algorithm. FCM is used to
produce an adaptive threshold on the
unknown region. To smooth the extracted
object, we used DCT-2D filter to remove
noises around the edge boundary. From our
experiments
in 10 video datasets and
perfomance evaluation conducted by MSE,
the result showed that an average increase in
accuracy of 31.55%. However, we found
that our approach was not so robust on
similarity of the color. Therefore, we would
combine this algorithm with optimization of
the cost function on the alpha region based
on spectrum which are expected to improve
the performance of object extraction
algorithm.

REFERENCES
[1] M. Hariadi., L. Huichien, and T. Aoki.,
“Semi-Automatic
Video
Object
Segmentaion Using LVQ with Color
and Spatial Features,” IEICE Trans on

Information and System, vol. E-88D, no.
7, pp. 1553-1556, 2005.
[2] Kosch. H, Distributed Multimedia
Database Technologies supported by

98 KURSOR Journal Vol. 7, No. 2, July 2013, page 89-98

MPEG-7 and MPEG- 2, Washington
D.C. : CRC Press, 2003.

Advances in Neural Information
Processing Systems, 2005.

[3] L.
Chiariglione,
“The MPEG-4
Standard,” Journal of China Institute of
Communications, pp. 54-67, September
1998.

[12] S. Yu and J. Shi, “Multiclass Spectral
Clustering,” in Proceedings of Ninth
IEEE Conference on Computer Vision,
Nice, France, 2003.

[4] R. Koenen, F. Pereira, and L.
Chiariglione, “MPEG-4: Context and
Objectives,” Signal Processing: Image
Communication, vol. 9, no.4, pp. 295304, 1997.

[13] L. Zelnik-Manor and P. Perona, “SelfTuning Spectral Clustering,”
in
Proceedings of Advances in Neural
Information Processing Systems, 2005.

[5] A. Bovic, The Hand Book of Image and
Video Processing, San Diego :
Academic Press, 1998.
[6] E. Şaykol, E. Güdükbay, and O. Ulusoy,
“A Semi-Automatic Object Extraction
Tool for Querying,” In Proceedings of
the 7th Workshop on Multimedia
Information Systems (MIS '01),, Villa
Orlandi, Capri, Italy, 2001.
[7] A. Levin, D. Lischinski, and Y. Weiss,
“A Closed-Form Solution to Natural
Image Matting,” IEEE Transactions on
Pattern
Analysis
And
Machine
Intelligence, vol. 30, no. 2, pp. 1-15,
February 2008.
[8] J. Wang and M. Cohen, “An iterative
optimization approach for unified image
segmentation
and
matting,”
in
Proceedings
of
Tenth
IEEE
International Conference on Computer
Vision (ICCV), Beijing, 2005.
[9] T. Porter and T. Duff, “Compositing
digital images,” Computer Graphics,
vol. 18, no. 3, pp. 253-259, 1984.
[10] A. Levin, A. Rav-Acha, and D.
Lischinski, “Spectral matting,” IEEE
Transactions on Pattern Analysis and
Machine Intelligence, vol. 30, no. 10,
pp. 1699-1722, 2008.
[11] K. Lang, “Fixing Two Weaknesses of
the Spectral Method,” in Proceedings of

[14] A. Ng, M. Jordan and Y. Weiss,
“Spectral Clustering: Analysis and an
Algorithm,” in Proceedings of Advances
in Neural Information Processing
Systems, Cambridge, 2001.
[15] D. Tolliver and G. Miller, “Graph
Partitioning by Spectral Rounding:
Applications in Image Segmentation
and Clustering,” in Proceedings of IEEE
Int’l Conf. Computer Vision and Pattern
Recognition, 2006.
[16] T. Roos, Fuzzy Logic With Engineering
Applications, Third Edition, John Wiley
& Sons, 2010.
[17] W. Pennebaker and J. Mitchell, JPEG –
Still
Image
Data
Compression
Standard,
Newyork:
International
Thomsan Publishing, 1993.
[18] R. S. Basuki, M. Hariadi, and R.
Pramunendar,
“Fuzzy
C-Means
Algorithm for Adaptive Threshold on
Alpha Matting,” in Proceedings of
Computer Society Coference on
Information Technology and Electrical
Engineering, Yogyakarta, Indonesia,
2012.
[19] C. Mythili dan V. Kavitha, “Color
Image Segmentation using ERKFCM,”
International Journal of Computer
Applications,
vol.
41,
2012.